They do look for it, obviously its less complicated if an EA has sole agency and they are also guarnteed the full commission on sale of the property with no competition.
But there are disadvantages for the seller as well, two times the advertisings fees, and potentially additional EA fees also (say EA1 arranges viewings and a potential buyers makes an offer to EA2 on foot of the viewing arranged by EA1 - Does EA 1 have a valid claim for fees?).
The two EA's would need to be communicating well to ensure no crossover and if in competition with another EA would the EA devote more time to selling a different property the full fees for which they would get? I think so.